Question

PLS HELP ME OUT ON THIS QUESTION. I’m trying to study!

Answer 1

Answer: 3

Explanation:

We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:

`(hypotenuse)/(leg)=(leg)/(part)`

where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.

Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.

Let's plug in these values:

`(13)/(z)=(z)/(9)\\117=z^2\\z=√(117)`

117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.

`z=√(9*13)\\z=√(9)*√(13)\\z=3√(13)`

The "?" must be a 3.